Reducing uncertainty in conceptual prior models of complex geologic systems via integration of flow response data

A major source of uncertainty in subsurface flow modeling is related to the conceptual model of geologic continuity that is adopted by geologists and hydrogeologists. Traditional model calibration methods usually rely on a given model of geologic continuity that is used to constrain the spatial distribution of aquifer properties. Flow response data, however, may also be used as additional source of information to constrain and revise conceptual geologic models or parameters that control them. The problem is more complicated when models that exhibit complex non-Gaussian spatial connectivity patterns are considered. We formulate the problem of flow data integration to select conceptual geologic scenarios with complex lithofacies as a regularized least-squares problem. The solution approach combines learning with model selection regularization techniques, where the former imposes geological feasibility while the latter eliminates scenarios that do not contribute to reproducing the flow response data. Geologic feasibility constraint to preserve complex connectivity patterns is enforced through supervised machine learning while geologic scenario selection is implemented via a mixed l(1)/l(2)-norm regularization term. The least-squares minimization is performed using an alternating directions algorithm that involves a sequence of model selection steps followed by geologic feasibility mapping, the latter implemented by combining k nearest neighbor (k-NN) algorithm with a pattern-learning method. Several examples with complex fluvial channel models are used to illustrate the performance of this approach.